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Royal nstitute of Philosophy

The Problem of InductionAuthor(s): James CargileSource: Philosophy, Vol. 73, No. 284 (Apr., 1998), pp. 247-275Published by: Cambridge University Presson behalf of Royal Institute of PhilosophyStable URL: http://www.jstor.org/stable/3752078.

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The Problem f nductionJAMES CARGILENo one doubts that philosophers have discussed at length the prob-lem of induction', but it would also be generally recognized thatthere would be disagreement as to precisely what that problem is.Rather than tackle the formulationproblem, I will borrow from apopular text:Our existence as well as science itself is based on the principle ofinduction that tells us to reason from past frequencies to futurelikelihoods,from the limited known of the past and presentto theunknown of the past, present,and future .. But though inductiveprobability is psychologically inescapable, we have trouble pro-viding a rational ustification for t.'We might say, then,that there is such a practice as induction, and aproblem associated with it is that of justifying engaging in it. Weengage in reasoningfromthingswe know about the past and presentto conclusions about the past, present and future.We can't resistdoing this but we have trouble finding a rational justification fordoing so. This problem suggests a generalization. We engage in rea-soning, reachingnew conclusions. It would be hard to resistengag-ing in this practice. How do we provide a rational justification forit?It seems appropriate to respond to such a question with theobservation that some of our reasoning is not justifiable, beingbadly done. It should be beyond dispute that an attemptto justifyall reasoning generically would be hopeless. Less indisputable,though also true, s that the ustification of conclusions which are infact ustified is not generic either, and depends on the particularcase. Against this, it may be said that there has to be somethingcommon to all justified conclusions which are justified, which iswhat would be sufficient o cite in response to the challenge to jus-tify hat conclusion. The inclinationto such a view as thismay seemto be one which twentiethcentury philosophy has thoroughlydis-pelled. But this is not as clear as it might seem, especially when wego back to the subclass of conclusions supposedly marked off bycalling them inductive. Some think that these are a special class of

t The Theory fKnowledge, lassic and Contemporaryeadings, ouis PPojman (ed.) (Wadsworth, 993),430.Philosophy3 1998 247

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James Cargilejustified conclusions. Others think that they are a special class ofconclusions such that those of them which are justified require ageneric kind of justification. But one of the most interestingfea-tures of this topic is thateven philosophers who reject the idea of ageneric justification for induction end up offeringwhat, if correct,would have to be just that. This is a phenomenon worth study,which might help explain why induction is such a perennial sourceof philosophical puzzlement.Hume asked 'What is the foundation of all conclusions fromexperience?' His answer was that such conclusions have no founda-tion in reasoning. 'All inferences from experience ... are effectsofcustom,not of reasoning.' (p. 57) This mightbe merelya certain useof 'reasoning' which sounds peculiar to those of us who use thetermdifferently. is sayingthat causes and effects re discoverable,not by reason but by experience' could be taken as a more or less'reasonable' pronouncement of empiricism. More reasonable: whatwill happen cannot be deduced frompremises solely about what hashappened with logical validity.This claim, that there is 'no neces-sary connection' between what has happened and what will, needsexplaining, but it has a basis in truths about necessity.It is even true that Hume had some reason to think this trueobservation about necessity was denied by historical rationalists.For they are associated with the idea that laws of nature must benecessary truths. Here there is a danger of misunderstanding.Aristotle means by a necessary truth, proposition that is true at alltimes. Even this saying is ambiguous. All truepropositions are trueat all times, in the proper understanding of these matters. Butignoring that for now, a proper natural law, in the Aristotelianscheme, would be that all A's always turnout to be B's, not just upto or during a certain time period. Being timeless in thisway just isbeing necessary in the Aristotelian sense. In this sense it is perfect-ly reasonable to require natural laws to be 'necessary'.However, some time before Hume there began a trend to themodern notion of a necessarily true proposition as one the falsity fwhich is inconceivable. In this sense, laws of nature are not neces-sarilytrue-their falsity an be imagined. Thus it could have struckHume as a discoverythat causal connections are not logically neces-sary connections-a discovery rather than a triviality.This couldhave been all right. But Hume goes from aying that natural laws arenot truths of reason to saying that theyare not based on reasoning.He goes on to say that predictions about the future are founded, ifat all, on habit. So the doctor who predicts that the patient cannot

2 An Enquiry ConcerningHuman Understanding The Liberal Arts Press1995), 46.248



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The Problem of Inductionrecoverwithout ntibiotics nds up with the same generickind of'foundation' orhis belief as the quack who saysthatthe patient'sonly hope is a dose ofhis snake oil.Of courseHume, beinga profoundlyntelligentnd reasonablethinker, oes tryto mitigate he absurdity f his result.But he isswimmingwith n anchor-his assumption hat ll reasoning boutpredictionsmusthave some basic principle hatprovides commonjustification orall cases thatare ustified.He speaksof findingcombination o have held in the past (past A's have been B's) andthenexpecting utureA's to be B's. He says this formingf expec-tationcannotbe by any processof reasoning nd thatthis princi-ple' is notfoundedon reason,buthabit. When we see lots of A'sturn ut to be B's,wedevelopthehabitofexpectinghis onnectionto continue.The observation hat his s not true n generalmightnot troubleHume. He could say that some constantconjunctions ead us toform abitsof expectationnd some do not. But hehas come to theconclusionthatthese expectations re all of themwithout ounda-tion in reasoning.This is unwarranted,nd maywell be due toassumingthat unless theprincipleof assumingfutureA's to turnout like past A's is a trueprincipleabout rational nference, o'inference' ittingts form an be anything ut a habitof expecta-tion,rather han a rational nference.Hume's pessimism bout theprospect orfinding rational asisfor xpectationsbout the future r evenabout thepresentbehav-iourofphysical bjects s hardto assess because he does take sometroubleto allow that some expectations re wiser than others.Hedoes not endorsethe view that hequack'shabitsofexpectationrejust as good as thedistinguished hysician's.n fact,when tcomesto respecting eputation, e is quite conservative.He just avoidscallingthewiserexpectation ne better ounded nreasoning. hisraisesthepossibility hat he is engaging n an idiosyncratic se of'reason' which would leave the translation f his views intomorenatural verydayanguage n the handsof scholars.One prominent ummarizer f Hume's epistemology s W. V.Quine. Quine characterizes ume as havingheld the ustificationfconclusionsabout 'bodies' to depend on translatinghe claims inquestion ntopurelysensory erms' nd thendeducingthemfromotherpurely ensory laims which were not susceptible o doubt.Quine seems to regardHume as havingbeen somewhat uccessfulintranslatingut a failure tmaking herequireddeductions.

Whatthen of the doctrinal ide, the ustificationf our knowl-edgeof truths bout nature?Here Hume despaired.Byhis iden-249



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James Cargiletificationfbodieswith mpressions edid succeed nconstruingsome singular tatements bout bodies as indubitable ruths, es;as truths bout impressions, irectly nown. But generalstate-ments, lso singular tatementsbout thefuture, ainedno incre-mentof certainty y beingconstrued s aboutimpressions.3

In addition o this view as to the nature f Hume's thinking boutjustification, uine seems to express ome considerable greementwith he deas as he characterizes hem:On thedoctrinal ide, I do not see thatwe are anyfartherlongtodaythanwhereHume left s. The Humeanpredicaments thehuman predicament.

This seems to be saying hat, mongother hings,Hume was cor-rect to despair of justifying ny singularstatements bout thefuture.WhetherHume did so despair s a scholarly uestion willnot pursue. There is,of course,the related cholarly uestion as totheproper nterpretationfQuine's remarks. he quotationsfromHume and fromQuine conflictwith what I take to be plain andobvious facts bout ustificationnd reasonableness.Withoutfur-therenquiry s to whether heirremarks eally remeantto applyto thesefacts, proposetoconsider n exampleof such a fact.Suppose thata groupof people have had an ongoingdiscussionof theprospects f BillBoggs' winning he Boston Marathon.Mostaresceptical fBogg's chances,butSmiththinks e can win.Boggswas seventeenth woyears ago and ninth ast year and has beenlooking trongnrecent ompetitions. ones eads the factionwhichdenies thatBoggshas anyreal chance ofwinning.On the eveofthemarathon, mith s holdingforth o a gathering f friends n hisconfidencehatBoggswill win.Jones, rrivingate, aysgrimlyNo,Boggs is notgoingto win tomorrow'. What makesyou so sure?'saysthecheerful mith. Well,' Jonesreplies,Boggs was in a badcar crashthis fternoon. is hipis smashed, ompoundfracturesfboth egs, puncturedung-he is in a coma at thehospital ninten-sive care.Here we have a singularstatement bout the future-that BillBoggswill notwin the Boston Marathon tomorrow.t seems thatHume's position s thatSmith'sassertion f thishas nobasis inrea-son,andQuine's position s that t s correct odespairof ustifyingsuch a conclusionas Smith's. In so faras this s a true account ofwhatthesephilosophers resaying,whatthey ayflies nthefaceofsuch facts s that nthiscase,thesingular redictions entirelyea-

'Epistemology Naturalized' reprinted in Naturalizing Epistemologysecond edition, edited by Hilary Kornblith (MIT, 1994), 15-31, p. 17.250



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The Problem of Inductionsonable and fully ustified. Jones is justified in being absolutely cer-tain that Boggs will not win. He is at least as justified as he is inbelieving that all bachelors are unmarried or that 7+5=12.This is not to say that Jones would be at all justified in regardingit as logically impossible that Boggs will win. If Jones is intelligentand well educated, he should be able easily to imagine a consistentscenario in which Boggs recovers overnight and goes on to win.Again, we can consider a second version of this case, in whichSmith has had religious reasons forhis claim that Boggs will win,claiming that God will help Boggs. If Smith responds to Jones'news by saying that he is convinced that God is going to heal Boggstonight,then I, forone, would not question that it is in the powerof God to produce such a miracle. Merely citing the severityofBoggs' injuries would not sufficeto answer doubts based on suchconsidcerations.Whether the fact that Smith has fervently rayed for the miracu-lous recoveryof Boggs would provide a basis for doubting Jones'conclusion need not be considered further. n the case under dis-cussion, the firstone, there is no prayer for recovery or religioushopes for t. There is no doubt about Boggs not winning and thereshould be none. It is perfectlyreasonable and justified to concludethat Boggs will not win. If asked for a reason for that conclusion,then the statement of Boggs' injuries is overwhelmingly adequate.One could question whether the reportsare true. But to granttheirtruth and then doubt the conclusion would be irrational.My use of 'fact,'heremaywell be challenged on thegrounds thatthe case is purely imaginary. It is not intended to be purely imagi-nary,but primarily s a convenient version of countless actual caseswhich could be found. We could say that specific names have beenchanged to protect the innocent. The fact is that there are lots ofcases relevantly ike the one described. With respect to such cases,Hume's talk of the absence of a foundation in reason makes senseonly to the extent that he means thatthe conclusions are not 'truthsof reason', that is, necessary truths. And Quine's talk of 'despair',makes sense only to the extent that he means despairing of anabsurd project. If the suggestion is that we should despair ofattemptingto ustifysuch conclusions as thatBoggs won't win, thenI must despair of making sense of the suggestion.However, we mightmove fromthe question whether the reasonsoffered forJones,conclusion are conclusive, to the question, whatreason we have forregarding them as conclusive. And then thingscan begin to look dark. Can we find a foundationin reason forhold-ing that the reasons offered are conclusive? I do not know of any.But surelyit is not ust a brute factthatsuch reasons are conclusive?

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James CargileI do not know. I claim only thattheyare conclusive, and thatin therelevant cases, there is no basis fordoubting that they are conclu-sive. No reason is needed for the reasons being conclusive. No rea-son could reasonably be requested.It may be replied thateven if it would not be reasonable to doubtthe adequacy of Jones' reasons, it is always possible to change thesubject, and ask, as a philosopher or general enquirer, why it is thatreasons of the sort offeredby Jones are so conclusive. You mightexplain that this is not intended at all to raise any doubt about theconclusion or the adequacy of the reasons, but just to express inter-est in the theoreticalquestion as to the nature of the adequacy.It seems quite reasonable to raise such a question, and it is nodoubt a failingin that field of enquiry to answer as I do, that I donot know any answer. The fact that no answer is required as a con-dition of the justification of Jones' conclusion is not an answer tothe furtherphilosophical question. But it should none the less be acaution to those who do trythephilosophical question, that twouldbe a severe defect n an answer if ithad the consequence thatJones'conclusion was not justified afterall. Unfortunately, t is commonforphilosophical discussion of justificationand reasoning to ignorethis distinction as to the limits of the enquiry.It is even common to simply characterize 'induction,' as a kind ofreasoning which cannot achieve certainty.One excellent and justlydistinguished textbookmay be cited merelybecause it is absolutelytypical. It is said:

A deductive argumentis valid when its premises, if true,do pro-vide conclusive grounds for the truth of its conclusion ... Aninductive argument makes a very differentclaim: not that itspremises give conclusive grounds forthe truth of its conclusionbut only that its premises provide somesupport for that conclu-sion.'This could be a genuine distinction of kinds of arguments. ThenJones' argument would be deductively valid, and some sketchyproofs in number theory mightbe inductive. But it is also clear thatthe texts take it to be necessary and sufficient ordeductive validitythat it be logically impossible forpremises to be true and conclusionfalse. On that meaning, Jones' argument is not deductively valid.Furthermore 'arguments' of the form P; therefore,P' are deduc-tivelyvalid even though the premise, even if true, provides no sup-port for the conclusion. What is worst, though, is that the texts are

'Introduction toLogic by Irving M. Copi and Carl Cohen, ninthedition,(Macmillan, 1994), 57.252



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The Problem of Inductiondrawn,by theirgeneral discussion, nevitably o theposition,notusually acknowledged, hat an argument uch as Jones' s 'induc-tive',withthe disastrous onsequence thatthey re holding hat nsuch an argumentt s not claimedthat hepremises onstitute on-clusive support. t is furtheraid of an 'inductive rgument' hat t'is one whose conclusion s claimedto follow rom tspremises nlywith probability, his probabilitybeing a matterof degree anddependentuponwhat elsemaybe the case.' (p. 60)Of course it is truethat n any argument,f it is claimed,as apremiseof theargument,hat the otherpremisesprovide conclu-sive support,and 'conclusivesupport,' s understoodto mean inpartthat f thosepremises retrue, hen he conclusion s true, henthe argument s deductivelyvalid (which is not to say that thepremisesdo provide conclusive upport). That is, any argument fthe formP1, P2, ... ,Pn,and if P1-Pn are true henQ istrue; here-foreQ', is trivially alid. And in anysincere rgument,hearguerbelievesthat f hispremises retrue, henthe conclusion s true. fthisbelief s added as a premise, hen heresulting rguments triv-iallyvalid. (If the claim of supportis added as a self-referentialpremise, s in If thisvery laim strue, henQ' wegetanothermat-ter,which s even ess relevant ere.)Butthis s not relevant ere.assumethatwhatwas intendedwas thatfor n inductive rgument,a reviewer hould not claim on behalf of theargument,hat t wasconclusive.This is a bad mistake,which can onlyhave a bad influence nteaching riticalreasoning.A propercharacterizationf argumentgenericallyhould make t a necessary ondition fbeinga conclu-sion that reasons be offered or t as conclusive, hat s, such as tojustify rawing hat onclusion. f thearguments not a good argu-ment, hen tmaybe false hat hepremises rovide onclusive ea-sons. But it is essential o beingan argument hat thepremisesbeput forward s providingconclusive reasons. To teach that aninductive conclusion is never really a conclusion should make'inductive' warning erm, n indication f bogusness.But that snot what s generallymeantby inductive'.This is not, however, o express any confidence bout what isgenerallymeantby inductive'. For 'deductively alid' we have theimpossibilityfpremises rue, onclusionfalse.This definition asits critics.Some complainabout the vaguenessof 'impossibility'othersabout the concept's paradoxical insensitivityo relevance.Furthermore,t is a definition nlyof 'deductively alid', not of'deductive'. t seems there re invaliddeductive rguments.By contrast,hedefinitions vailablefor inductive', o not focuson the successful ase. The mostcommondefinitionor smallfam-

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James Cargileily of definitions) is by referenceto the practice of concluding thatfutureA's will behave like past A's in respect of turningout to beB's. This is what Hume called a 'principle' and treated as needing,but not having, a basis in reason. Anthologized writers on inductiongenerally relatethemselves somehow to some version of thisprinci-ple (PI). Here is Bertrand Russell's version of PI:

(a) The greaterthe number of cases in which a thingof the sortA has been found associated with a thingof the sort B, the moreprobable it is (if no cases of failureof association are known) thatA is always associated with B; (b) Under the same circumstances,a sufficientnumber of cases of the association of A with B willmake it nearly certain thatA is always associated withB, and willmake this general law approach certaintywithout limit.5

Russell holds that this principle cannot be proved or disproved byexperience, and that it is a fundamentally mportant principle.All arguments which, on the basis of experience, argue as to thefutureor the unexperienced parts of the past or present, assumethe inductive principle; hence we can never use experience toprove the inductive principlewithoutbegging thequestion. Thuswe must eitheraccept the inductiveprinciple on the ground of itsintrinsic evidence, or forgo all justification of our expectationsabout the future.If the principle is unsound, we have no reasonto expect the sun to rise tomorrow .. or to expect that f we throwourselves off the roof we shall fall. (pp. 68-9)

This is an extravagantclaim about the consequences of the princi-ple's being unsound, considering that it appears on its face to beunsound. A famous example of Russell's own will suffice to bringout this appearance: 'The man who has fed the chicken every daythroughout ts lifeat lastwringsits neck instead, showing that morerefinedviews as to the uniformity f naturewould have been usefulto the chicken'. (p. 63) Useful or not, similar refinement s neededto save Russell's principle. Otherwise, we simply let A=a morningin the life of the chicken, and B=a morningwhen the farmerhas fedthe chicken and not wrung its neck. We need not enquire as to thethought processes of the chicken. The farmerand we philosophersas well all know thatin a substantial number of cases 'a thingof thesort A has been found associated with a thing of the sort B'.Furthermore, 'no cases of failure of association are known'-remember that we are dealing with a specific case; that chickensgenerallydo not farewell in similar arrangementshas been leftoutin the formulation ust quoted. It clearly follows from Russell'sThe Problems of Philosophy Oxford, 1979), 67.

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The Problem of Inductionprinciple that it has daily been getting more probable 'that A isalways associated with B'. And this is absurd. At the very east, evenif you refuse to admit that the farmer knew all along that he wasgoing to kill and eat the chicken, (perhaps you appeal to scepticismabout the future)you could not reasonably hold that the probabili-ty of this not happening, and the chicken's being fed indefinitely,simproving daily.Russell does follow up withan argument which might be thoughtto answer this objection. He stresses that probability is always rel-ative to certain data'. Thus a man who concludes in accordance withRussell's principle, after seeing a great many white swans, that it isprobable hat all swans are white, is not shown unreasonable by thediscovery of black swans in Australia.

A man mightknow that colour is a veryvariable characteristic nmany species of animals, and that therefore, n induction as tocolour is peculiarly liable to error.But this knowledge would be afreshdatum, by no means proving that the probability relativelyto our previous data had been wronglyestimated.Applied to the chicken case, the farmerwould have additional databeyond thefacts about regularityof feedingand non-wringing.Thechickenmightbe theproper thinkerfortheexample after ll. It pre-sumably has been given no reason to suspect thatthe farmer s any-thingbut concerned to keep itwell fed.This defence of the chicken's reasoning is not compatible withthe claim that 'more refinedviews as to the uniformityof naturewould have been useful to the chicken'. The chicken was presum-ably doing as well as could be done on the information available toit. What it needed was more informationabout farmers.However,just how such informationmighthave been used is leftcompletelyundetermined by Russell's principle.Russell's defence is unclear,but the best that can be made of it isto take it as restricting he application of his principle to cases inwhich you have no other relevant information than that past A'shave been B's. This gets him out of the farmercase, because thefarmerhas otherrelevant nformation.But then Russell's claim thatthe reasonableness of our expectation that the sun will rise tomor-row depends on his inductive principle is indefensible, since it isclearlyfalse that the only relevant nformationwe have about that isthat it has always happened in the past. Justas we can use our rele-vantbackground information o predict thatthe chickenwill not getfedtoday despite the factthatitalways has, we (rather, stronomers)can use relevantbackground information o predict thatthe sun willrise tomorrow.

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James CargileFurthermore,the picture of someone knowing only thatpast A'shave been B's is deeply obscure, so that the principle not only doesnot apply in everyday cases; it is not clear that it applies in anycases. We may tryto imagine ourselves in a situation like the chick-en's, prisoners of a power we do not understand, which brings usfood every day. Is it reasonable for us to infer that the power willcontinue to do so? We may as well go out to the feeding place whenhungry-what else is there to do? If escape were an option, itwould be a differentmatter. We may have no basis whatever fortheorizing about our food supply.Russell's principle is either triviallyfalse or useless. It is triviallyfalse taken literally.Modified so that it licenses concluding the nextA will be a B when past A's have been, etc, and the other availablebackground information is favourable, it is useless. Such vaguequalifications as 'relative to proper background information' or'given an adequately large sample' can be interpretedso loosely asto make the 'principle' trivially immune to counterexample, butquestion-begging to apply and hence useless.6 To criticizeRussell'sposition adequately requires giving due weight to this fact. But it is

difficult o get thisweight right.Hans Reichenbach attempted to defend the PI by appeal to a fre-quency definitionof probability.'The probabilityof an A being a Bis the limit of the ratio of past A's that are B's to past A's, as thenumber of A's observed goes to infinity.Our best posit, accordingto Reichenbach, is to take the ratio observed so far as the probabil-ity.He stresses that we won't know this is the true limitratio; but ifthere is such a limit,this is our best hope of getting t right.This is false. To base my estimate of the probability of headswith a given penny on the observed ratio after, ay, 10 tosses, is to belikely to be mistaken about the true probability. It may be repliedthat we know this only because we know of trials that were suffi-ciently long which established the probability.But that is not howwe know the probability, or not the only way. One omission in thePI is any specification of a sufficientnumber of trials for setting agiven probability level. Without that the PI is useless. It is useless,but in making this clear it helps to note thatthe probability that allbaboons of a certain species have brightlycoloured buttocks,basedon seeing four healthy specimens, an adult male, an adult female,and a young female and an old male, can be set close to 1 withmorejustificationthan forsettingthe probabilityof heads based only on

6I have discussedthetrivializingffect fqualifications o the PI in OnHavingReasons',Analysis 966, 189-92.'Page referencesre to theexcerpt rom xperiencend Prediction hichis included n The Theory fKnowledgeditedby Louis Pojman.256



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The Problem of Induction10 tosses. We do of coursemake udgements bout how big a sam-ple should be. But we do nothave a generalprinciple overing llsuch udgments.The idea that the limit at infinity will be reached byReichenbach's approach if reachedat all is cold comfort ndeed,when we consider 1) it won'tbe reachedat all, being nfinite:nd(2) anyfiniteequenceofoutcomes, owever ong, s mathematical-ly compatiblewith ny imitprobability.Reichenbach's haracterizationf theaim of induction' s to finda probabilityn thesense of the mathematical ersionof thefre-quency theory-a limiting atio.His thought s that fyou alwaysassume thattheprobability f an A beinga B is theratioof pastAB's topast A's,then fthere s a limiting atio,youwillfind tthisway. This is a mathematical ruth.But you will not get to infinity,and theremaynot be a limiting atiowaitingfyoucould. And thefactthat theprobability f an A beinga B does turn out to be n(when the limitexists) maybe a pitifully oor guide to decidingwhether hisA isgoing o be a B, since thisA is also a C, D, etc. Andif this sn't all bad enough,Reichenbach ells us thathis approachis all the hope we have forrationalityn thepredictionbusiness.Evenhabit ooksgood bycomparison.In a well-known aper8 aul EdwardscriticizesRussellforhold-ing 'that unless we appeal to a non-empirical rinciplewhich hecalls "theprincipleof induction"'we must answer n thenegativesucha questionas

(1) Assuming hatwe possessn positive nstances f a phenome-non, observed n extensively ariedcircumstances,nd thatwehave not observeda singlenegative nstance wheren is a largenumber),have we anyreason to suppose thatthe n+lst instancewill also be positive?Edwards argues thatquestion 1) can be answered n theaffirma-tivewithoutnany way appealingto a non-empirical rinciple'.Tothisend he citestheexampleofinferringhat omeonewho has ustjumped from window on the fiftieth loorof the Empire StateBuildingwill fall towardsthe streetratherthan upwards. Thisexample should be comparedwith the one givenearlierabout aseverely njuredman not winninga marathon.That one was anoverwhelminglyeasonable nference,ne notopen to anyreason-able doubt. The onlyproblemwith he umper example ies n char-acterizing t as an inference t all. People have been observedtojump from he Empire State Building.But it is not obvious that'BertrandRussell's Doubts About Induction',Mind LVIII (April,1949), 141-47.

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James Cargilehorrifiedonlookers 'inferred' the jumper would fall. Rather, theysaw thatthe man was going to fall. (If the man had been wearing aparachute, and there was a windstormgoing on with a tremendousupdraft,thenthe case would be different.) t is obvious that in somecases of Empire State jumpers, expecting a fall is right,and actualcases can be cited. That this would be inferential s not so clear,though cases can be imagined in which thistoo would be the correctdescription. Recall Russell's claim: 'If the principle is unsound, wehave no reason to expect that ... if we throw ourselves off the roofwe shall fall'. This, as was argued, is false. The principle is unsound(if not hedged so as to be useless), and we do in some cases none theless have reason to expect, etc.This does allow a positive answer to (1) based on empirical obser-vations. Suppose we are observing a man on a ledge on the fiftiethfloor, about to jump. We say 'Oh no -this will be the 17th case ofsomeone jumping-he's going to fall to the street ust like the pre-vious 16 ' This is an empirical claim and is sufficient o warrant anaffirmative nswer to (1) interpreted s prefacedwith 'Does it everhappen that?'. For this is a case in which we have observed n(=16)positive instances and no negative, and we have reason to supposethat the nth(=17th) will be positive.It might be objected that in this case we do not have 'extensivelyvaried circumstances' since all our previous cases were fromthatsame building. This is worthnoting in connection with the vague-ness of such hedging phrases, but we can overridethe objection forpresentpurposes. For we could add all the known cases of fallsfrombuildings (while allowing forascending parachutistsand the like) toqualify as having positive instances observed in extensively variedcircumstances. This should be enough to establish Edwards' claimthat 'without in any way calling upon a non-empirical principle forassistance, we oftenhave a reason forsupposing that a generaliza-tion will be confirmedin the future as it has been confirmedin thepast'.However, this is assuming that the ambiguous quantification ofan affirmative nswer to (1) is taken as the modest 'It does happenin some cases that, with n positive instances, etc. we have reason toexpect n+1 to be positive'. It is verydifferentf we read the affir-mative answer as the claim that wheneverwe have n instances inextensivelyvaried circumstances,etc. thenwe have reason to expectn+1 to be positive. We may call the former, xistentialreading of anaffirmative nswer to (1), El, and this latter,universal reading, Ul.U1 is just another version of PI. To argue that Ul is an empiricaltruth is no improvement over Russell's claim that PI is an indis-pensable assumption. The question whetherPI is 'empirical,' is of258



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The Problem of Inductioncourse another topic for philosophical disputation. But the disputewould seem less urgent if it is recognized that PI is not even a truegeneralization.It seems clear that Edwards does not intend to argue for PI as ageneral truth. He speaks of showing that 'we often have a reason'never of always having a reason, when we have the n positives, etc.His examples and claims are eminently sensible. But he is not suc-cessful in extricating nductive ustificationfromdependence on PI.He centres his argument against Russell on the idea that Russell hastacitly given a high redefinitionof 'reason foran inductive conclu-sion', to mean 'logically conclusive reason'. And he replies that thisis not what is meant, and offers a characterization of what is the'main sense' of 'reason'.The charge against Russell is incorrect. Russell does not denythat we have reason in cases where we lack logically conclusive rea-son. Rather,he says that our having reason in such cases is depen-dent on PI, and he says that PI is not capable of being proved ordisproved by appeal to experience. Edwards picks Russell up on hisclaim that PI is nonempirical. This claim is hard to evaluate, and Ihave not attempted to do so. My objection was focused on thedependence claim. Being false or trivial,PI is useless in justifyinginductive inferences, so that none depend on it. Edwards slips(unintentionally, believe) into defending an affirmative nswer to(1), as if it were analytic. That makes his modest preference forElover Ul indefensible. About themeaning of 'reason foran inductiveconclusion,' he says:

According to this main sense, what we mean when we claim thatwe have reason for a prediction is that the past observations ofthis phenomenon or of analogical phenomena are of a certainkind: theyare exclusively or predominantly positive, the numberof positive instances is at least very large, and they come fromextensivelyvaried sets of circumstances. This is of course a verycrude formulation. But forpurposes of this article, it is, I think,sufficient. p. 358)Now, if that is the definition of the relevant meaning of 'reason',then an affirmative nswer to (1) comes to this:

Assuming that we possess n positive instances of a phenomenon,observed in extremelyvaried circumstances,and thatwe have notobserved a single negative instance (where n is a large number),then the past observations of this phenomenon or of analogicalphenomena are exclusively or predominantly positive, the num-ber of positive instances is at least very arge, and theycome fromextensivelyvaried sets of circumstances.259



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James CargileTo say that his s 'often' rue, rtrue n many ases, s absurd.Onthis nterpretation,1) is properly ead as Ul and El is confused.Note that El' and 'Ul' are onlyabbreviations ordisambiguationof the quantificationof (1). 'Reason' was left uninterpreted.Edwards' accountof the main sense' of 'reason' s whatmakes Ulexpress truth nd El an oddity rather ike Some contradictionsare false'-of course the trouble s not thatEl isfalseon this nter-pretation).Edwards is highly ensitive o thevarietyn use of 'reason'. Henotes,forone example,that omeonemightuse 'reason' merely oapplyto a positive nstanceof a generalization. his suggests hathe is concernedwith omethingmore, nhis main sense justify-ing reason.The topic s ustifyingnductive nferences,otshowingthat we can say that nduction ometimesprovidessome, even ifinadequate,reason.But even n the form f establishingust 'somereason',Edwards' claim about meaning s eitherfalse or trivial nthewayPI is.It is theclaimthat themere factthatpastA's havebeen B's, with no furthernformation,onstitutes dequate reasonto ustify oncluding hatthe nextA is more ikely hannot to be aB. My view s that his snever rue, f we do not consider he back-ground nformation e have associatedwithour conception f A'sand B's. And even considering uch information,t is onlysome-times rue hatpastinstances lone,underonlyone conceptA, givereasontoexpectthe nextA to be a B.9I agreewithEdwardsthat here re ots of cases in which,havingnpositive nstances,tc.,we are ustified n expecting +1 to be pos-itive. believe thatRusselldidnotdenythiseither. ut contraryobothRussellandEdwards, hold that nsuchcases,the reasons renotthe fact hat herehave beennpositives, tc.Forexample,whenJones ustifiablypredicts that Boggs will not win the BostonMarathon,his reason is that Boggs has been broken up in a carcrash.That is what ustifieshis conclusion. ts not thatn peoplehave been observedbrokenup in thatwayand havenot functionedwellshortlyhereafter,ndn is large nd the cases are varied, o wemayconclude there s reason nthis, he n+lst case. That mightbeundertaken ysomeone trying o provethatJones'reason s a goodreason,which s a risky xerciseperhapsquite honourably nder-takenby philosophers,hough ftenwithbad results.It would seem that asking about the meaningof 'reason,' or'inductivereason,' would help in clearing up puzzlementaboutinduction.But if I am right,t s noteasyto do thissuccessfully,sthe case of Edwards should suggest.Anotherphilosopherwho

For further rgument on this point, see 'On Having Reasons'.260



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The Problem of Inductionapproaches 'the problem of induction' in terms of meaning is P. FStrawson, who says: 'The only way in which a sense might be givento the question, whether induction is in general a justified or justi-fiable procedure, is a trivial one which we have already noticed. Wemight interpret t to mean 'Are all conclusions, arrived at inductive-ly, ustified?' i.e., Do people always have adequate evidence for theconclusions they draw?' The answer to this question is easy, butuninteresting; it is that sometimes people have adequate evidence,and sometimes theydo not.'10'Sometimes theydo and sometimes theydon't'-this suggests ananswer to Hume's question 'What is the foundation of all conclu-sions fromexperience?'(434), namely 'Some conclusions fromexpe-rience do not have foundations, being unfounded mistakes-and asfor the "basis" of those thathave bases, it dependson theparticularcase .However, it is all too easy to strayfrom thispath of particularismback into the puzzles of generality.Strawson's use of 'i.e.' in theabove quote suggests his rewording of (1) 'Are all conclusionsarrived at inductively, ustified?' should be (2) 'Do people alwayshave adequate evidence forthe inductive onclusions they draw?', towhich his answerwould be 'Sometimes theydo and sometimes theydon't'. But he immediately continues "'forming rational opinionsabout the unobserved on the evidence available" and "assessing theevidence by inductive standards" are phrases which describe thesame thing' (p. 258). If this were right,or were a stipulation as tohow Strawson will use 'inductive' then the answer to 2 would haveto be 'yes, trivially, y the definition of the terms'. That is at oddswith 'Sometimes yes, sometimes no'. Strawson might say thathe istalkingabout two different ses of the term inductive'; one mean-ing 'rational', the other meaning, say, 'concerned with the unob-served'. If so, he did not make thissufficiently lear,and there s evi-dence here of a temptationto use the same term n conflictingways.Besides the equation between being a rational method forassess-ing the evidence and being an inductive method, Strawson alsoemphasizes an importantrelation between being a successfulmethodand being an inductive one. He speaks, in referenceto a method, ofasking whether its employment is inductively ustified, whether itcommonly gives correct results' (p.258) as if these are the same.Again, 'by the very fact of its success it would be an inductivelysupported method'. Finally,he says:

So everysuccessful method or recipe forfindingabout the unob-served mustbe one which has inductive support; forto say that a10 Introductiono Logical Theory Methuen, 1952), 257.

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James Cargilerecipe is successful is to say that it has been repeatedly appliedwith success; and repeated successful application of a recipe con-stitutes ust what we mean by inductive evidence in its favour ...any successful method of finding out about the unobserved isnecessarily ustifiedby induction. This is an analyticproposition.(p. 259)

In addition to this analytic truthabout being inductive, there is alsosaid to be an analytic connection between being an application ofthe 'straight rule' and being inductive. Strawson says... it is an analytic proposition ... that other things being equal,the evidence for a generalization is strong in proportion as thenumber of favourable instances, and the variety of instances inwhich theyhave been found, is great. So to ask whether it is rea-sonable to place reliance on inductive procedures is like askingwhether it is reasonable to proportion the degree of one's convic-tions to the strengthof the evidence. Doing this is what 'beingreasonable' means in such a context. (pp. 256-7)

I will assume that Strawson means that known favourable instancessupport a generalization. If S has no good reason to thinkpast A'shave been B's, then the fact thattheyhave been need not guaranteethat it is reasonable of S to believe future A's will be B's. ButStrawson does appear to hold that the more you know pastfavourable instances, etc. then the more justified confidence youmay have that the future nstances will go the same, and thatmov-ing to such confidence levels is proceeding inductively.This suggests three equations. In formulating them I will use'method', as short for method or recipe forfinding out about theunobserved'. We haveEl. being a rational method=being an inductive methodE2. being a successful method=being an inductively justifiedmethodE3. being an application of the straight rule=being inductive.

All of these are representedas being analytic. There is some reasonto take Strawson as intendingE2 as only a one way entailment from'successful' to 'inductive'. Anyway, will only use it that direction.Strawson calls each of his three equations (or two equations andan implication) 'analytic', that is, truthsabout the meanings of theterms involved. This could help give being analytic a bad name. Itis interesting o note that each of these three equations could be saidto merely reflect facts about how the terms are used. But then theterms are seriously ambiguous. This is a danger in the use of the'analytic method'. Note that the equations amount to a strong262



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The Problem of Inductiondefence of the PI. Following the PI is by definition being inductiveand also is necessarily rational and is at least a necessary conditionof being successful at forming opinions about the unobserved onthe basis of past observations. (What then, has become ofStrawson's earlierwarning that the only sense available for the gen-eral question whether nductive inferencesare ustified is one whichmakes the appropriate answer 'Sometimes they are and sometimesthey aren't'?)Strawson gives an example in which someone uses a wild'method'-closing his eyes and guessing and 'it's usually (always)the rightanswer' (p. 258). But in his case, it appears that the guess-er has observed over a long term that this method does work forhim. It is hard to imagine this really happening for a completelyopen range of questions. The guesser would be findinghimself tohave godlike powers. But suppose we confine it to guessing whethera certain coin will land heads. As a 'method' forforming opinionsabout how the coin will land, guessing, at the outset (in a normalcase with no special antecedent information)would not be rational.Guessing would be as good as any other method, but not good. Ifforcedto bet on the coin, thenguessing would be a reasonable thingto do, but being sure you would be right,and being willing to actaccordingly,would not be rational.If you were forced to bet, or just idly tossing the coin, and younoticed thatyour guesses were always right, t would be reasonableto find this quite surprising. You might privatelytest the coin andthe ridiculous hypothesis that your guess is reliable. You might'find' thatyour guess is reliable forthis coin and onlythis one. Thatis, you might find that trial after trialyour guess is right,and thatthis does not happen for other coins. You could get in the positionof having good reason to believe the extraordinary generalizationsuggested by such observations. You would also have good reason tobe verycautious about talkingto anyone about it,knowing that theywould reasonably regard you as nutty.If you then were required to predict the outcome of a series oftosses of your coin, and you got the success rateyou would reason-ably expect and no longer find surprising, an amazed observermight ask you how you were doing this, what method you wereusing. You could then reply truly, My method is just to close myeyes and guess'. It might then seem that it must follow that thismethod is rational and also successful and thus a confirminginstance of one of Strawson's equations.In my opinion, this would be a mistake. Your method forarrivingat a prediction should not be identified withyourmethod for arriv-ing at a rational opinion about how the coin will land. The idea of a

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James Cargilemethod foracquiring opinions makes some sense, but it is hard tomake sense of guessing as being such a method and it is surelynota method of justification. Your justification is not merelythatyouso guessed, but all the considerations that have led you to believethat your guesses about this coin somehow turn out correct.It mightbe replied that,none the less, the method of guessing isa rational one to use, and a successful one, so the equation in thiscase is not in question. This would overlook the point that it is nota method for ustifyingor founding opinions about the unobserved,or even a method forforming opinions. Guessing does not requirebelieving (it can of course include believing, but that is in this casemerelya distraction I will not bother to workthrough). It is in thiscase just a method for arriving at predictions, and predictionsshould not be confused with udgments.It must be admitted that this distinctionis especially easy to losetrack of in connection with predictions to oneself, since philoso-phers are sometimes tempted to regard believing as saying to one-self. This makes it difficult o imagine how someone could private-ly experiment with the coin and learn that his predictions are alwayscorrect, and only then come to believethey are always correct. Forhis sayings to himself, that is, his predictings, would be confusedwith beliefs by the innersaying model. We could, of course, have itthat the man is actually forming opinions about how the coin willland. Since we are dealing in mere logical possibilities, it costs noth-ing extra to have it that way. But it is better to stickto what is min-imally required to be guessing. One can say to oneself 'Its going toland heads'. An audience helps make this into a prediction, but isnot essential.

To give an analysis of 'A guessed the answer to the questionwhetherP, would be a difficult roject. Suffice it to say that n somecases, one guesses merely by forcinghimself to answer the questionwhen he has no opinion as to the truth of the matter. The coin iscovered, and you are asked whether it is heads and you say 'Okay,I'll say it isn't, this time'. It is not surprisingthatyou may turn outto be right.But ifyou turn out to be rightfor an extraordinaryrun,that is extraordinary.Then, knowing that that has happened maygive you reason to think thatsomehow, your guess is a good indica-tion of the state of the coin. Now, the fact thatyou said 'It's heads'is good evidence that t is indeed heads. But it is incorrect o say thatso saying is a method forforminga belief on the question whetherit was heads. You form the belief by considering, among otherthings,the fact thatyour guessings have been extraordinarily ccu-rate.We may say, then, that by the method of guessing, someone has264



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The Problem of Inductionbeen successful at making true predictions, but this is not a licensefor saying that guessing has been a basis for formingustified beliefsabout what will happen. It is knowing about the success of the pre-dictions and having reason to doubt that the past success can beexplained as mere coincidence that ustifies believing that the pre-dictions will continue to be true. And that is not mere guessing.What if our guesser is completely convinced he is getting t right,but without observing that he is? What is observing here? He toss-es the coin and doesn't even bother to look at the result. He is sosure his guess is rightthat it seems to him pointless to bother tocheck (and he thought it pointless from the outset, not just afterdeveloping reasonable confidence based on his success rate). Likethe man who has checked and found the coin to be landing as heguesses itwill, this one believes he has had a long run of successes.The difference s that this belief is not reasonable, so that the con-clusion based on it, that he will continue to be right, s not reason-able either.The guesser is not learningof his success, just having it.Surely this does not qualifyhis procedure as rational. If it qualifiesas followingthe PI, then so much the worse forthe PI. If someoneformsthe unreasonable opinion thatpast A's have been B's, is it thenreasonable of him to infer that the next A is likely to be a B?Whichever way this is answered, the case is a problem forStrawson's equations. For even if to qualify as followingthe PIrequires knowing how things have been turning out in past cases,this man is just as successful as if he were being rational and fol-lowing the PI, so that E2 entails that he is followingthe PI. Rulingout the case would thus only involve further nconsistency.This shows thatthe threeequations cannot be correct. Our luckyguesser is following a 'method' for making judgments about theunobserved on the basis of his alleged 'observations' which is suc-cessful and thus inductive by E2. Whether or not it qualifies as fol-lowing the straight rule it clearly should not qualify as rational.Strawson's three equations cannot all be truths about one and thesame meaning of 'inductive'.This criticism was based on just the one way reading of E2. It isinteresting, n passing, to enquire whether, n addition to its beingpossible to be successful without being rational, it is possible to berational without being successful. However, this question is cloud-ed by the Kantian point that success in formingexpectations aboutthe future is a necessary condition of being a normal person. Torecognize your surroundings,on thisview, requires expecting thingsto behave as things of those kinds should. Just walking down thestreet, you expect that the pavement will not rise up and seize you,or the ground give way under your step, or your foot turn into a

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James Cargiledragon, etc., etc. If these 'inductive expectations' were not 'suc-cessful' you would not exist as an integrated personality.There is a lot of truth n this picture. It provides some basis forthe editorial quotation which began this paper ('Our existence ... isbased on the principle of induction'), but it overintellectualizeswalking down the street. It is perhaps true that one expects, e.g.,thathis head is not going to turn into a pumpkin, and even true thatthere is some justification for this expectation. Still, if someone isasked to justify such an expectation, he will be at a loss. And heshould be. The philosopher may be able to work up a patter pur-porting to rationalize the expectation, and the psychologist mayproduce a correct causal account of how normal people come tohave such expectations, but the fact is that such expectations are inthe overwhelmingrunof the time notoccasions forreason-givingatall and are not cases of forming xpectations on the basis of reasons.That countless expectations are not shattered as theyare when onemeets up with a mugger, etc.) is indeed a condition of our healthyexistence, but we should not characterize this as the requirementthat induction be justified or even successful.

Strawson says that to say that a recipe is successful is to say thatit has been repeatedly applied with success'. Then no recipe couldbe successful on its firstapplication. Presumably it would not beunsuccessful on the firstapplication either, no matterwhat hap-pened. So what would it be fora recipe or method to be unsuccess-ful? It would seem to be being repeatedly applied without success.The argument runs: 'repeated successful application of a methodconstitutes ust what we mean by inductive evidence in its favour'and repeated successful application is also what we mean in sayingthe method is successful; therefore a method which qualifies asinductive will be successful.This argumenthas already been challenged on the grounds thatthe method of relying on a method which you know has beenrepeatedly applied successfully is not automatically the samemethod as the one you have been repeatedly applying successfully.The method of relyingon long term successful methods may bemade out as the method of followingthe straightrule,where in thiscase the past A's that have been B's are past applications of methodX which have been successful. It was observed that method X maywell not be based on the straightrule itselfand may be a method itwould be idiotic to trust ndependentlyof considerable evidence ofits successful application. The successful long termapplication of amethod X does not prove thatmethod X, in itself, s a rational oneto employ. It is just that it may in certain possible cases be rationalto employ methods,however silly theymay seem, if theyare known266



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The Problem of Inductionto work over a long run. But appeal to that need not be appeal tomethod X.Now we need to turn to the question as to what we can concludefrom repeated unsuccessful application of a method. Could weconclude that the method is not a rational one to employ? Supposethat someone applies the straightrule to conclude the next Al willbe a Bi. To qualify as employing this rule he has to have observeda sufficientsample of Al's and found them to be Bl's. He has notjust jumped to expecting any old Al to be a Bl without carefulcollection of 'enough' examples. But despite all his excellence insampling, he is mistaken-the next Al is not a Bl. This does notshow he was not rational, nor that the straightrule is unsuccess-ful.He then turns to the question as to whether A2's are B2's. Againhe does a painstaking ob of sampling and finally oncludes the nextA2 will also be a B2. Wrong again But who's to blame him? Thiskeeps up until one day, having seen an impressive number of A78'sturn out to be B78's, and preparing to venture a prediction, hethinks 'Wait a minute According to my records, this is the 78thtime I have applied the straightrule, and in the previous 77 cases, Igot beat. This darned rule just isn't workingfor me.'What can we say to this sensible but unlucky soul? Suppose thatwe had been checking each one of his (inductive?) inferences to seewhether his sample looked good. We have always found he wasdoing a terrificob, but have not stayed around to see how it turnedout. It would be a job to make this story plausible, but maybe wehave lots of predictorsto check up on and we have been ordered ustto check the basis and thenget on to the next customer, etc., etc. Wewould then be quite reasonable in expecting that most of this man'spredictions have been right.We might in fact be stunned to heartheywere all wrong, perhaps incredulous. Should we conclude thathe has not been proceeding inductively,or that his reasoning hasbeen bad, or that he has been applying a bad method?We might trythe observation that our inductor has had countlesssuccesses, going back to the idea that his expectation that trees willnot jump out of the ground and dance on their roots this time isbased on the past stringof cases in which they have not behavedthat way, etc., etc.. This should be ruled out by our emphasis oncases in which an argument is actually presented, accompanied bythe explicit assertion of a conclusion.We could complain that, knowing he has failed in 77 tries, heshould have begun sooner to factor in that consideration in theargumentshe has been presentingus for review. We mightnot haveendorsed his 70th prediction so enthusiastically if we had known

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James Cargilehow the previous 69 had turned out. One might even try to avoidgranting that he has been following the straight rule and beinginductive, on thegrounds that he should have been keeping trackallalong of how it is going withC's being D's where C=application byme of the straightrule and D=successful application.This reply involves a shift in the interpretationof the PI, toinclude taking into account the problem of the reference class. Inconsidering whetherX is a B, you may not simplynote that X is anA and survey past A's. You must also note whether t is a C and con-sider the performance of past C's. You mightas well also be expect-ed to decide which referenceclass, A's or C's, is the best guide to X.On this interpretation, it is indeed impossible for the PI to beapplied unsuccessfully.But this is arranged by trivializingthe ideaof 'application of PF'.I will defer to this so far as to refrainfromclaiming thatit is pos-sible forthe straightrule to be unsuccessful. But this is only due tothe obscurityof the rule. Once we bring in the 'problem of the ref-erence class' it is a misleading pretence to speak of following thestraight rule. When it is just a matterof past A's being B's, then itis possible thatsomeone followingthe rule could have a long run offailures, once we stress that the applications are not in formingtheexpectations that are the source of the unity of experience butrather, formal pronouncements of predictions. But if we requirethat in asking whether thisA, x, is going to be a B, we consider, notonly the past recordof A's but of anyother class towhich x belongsand which may be relevant,then the procedure is altogetherdiffer-ent. We make it possible to rule out the possibility of long run fail-ure by building an escape clause in the procedure fordeterminingwhat counts as an application in the firstplace.The 'problem of justifying nduction' is sometimes characterizedas the problem of justifyingbelieving thatthe futurewill be like thepast. Whether all induction is concerned with the future s a cloudyquestion we do not need to answer. It may be argued that even whenwe inductively conclude, say that primitivepeople inhabited a cer-tain region, this essentially involves some prediction about howfuture observations will turn out. This seems doubtful, but neednot detain us. It is enough to observe that the slogan that the futurewill be like the past (call that FPI) is verylike the P1 in the role it ismistakenlythoughtto play in inferences about what is going to hap-pen. Paul Edwards argues as follows:

In the ordinarysense of the word 'future'therefore,what Russellcalls past futures are futures.They are futures n relation to cer-tain other periods which preceded them. Now, the appeal to thefactthatpast futures resembled past pasts and past presents con-268



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The Problem of Inductionstitutes excellent inductive evidence for the conclusion that thefuturewill resemble the past and the present. (p. 359)

This is, like Edwards' answer to his question (1), an answer thatturns out, however intended,to be a genericdefence of the principleFPI, and thus an unindiscriminating one. Edwards would certainlypoint out that the futureoftendiffers n strikingrespects from thepast and thatnot all expectations of similarity re justified. But hisargument, aimed at Russell, applies to just the sort of generic usti-fication he elsewhere avoids claiming. On the question of FPI, heendorses the argumentof an earlier paper by F. L. Will. Will's pri-mary concern is with scepticism about the future. Future A's arelikelyto be B's because past A's have been B's, and the future willbe like the past-in thatrespect at least. Hume oftenspeaks in theseterms, worrying that the past may be no rule forthe future' (435).I have been arguing that it is a mistake to suppose thatthe rational-ity of predictions depends on the truthof such a general rule as PIor FPI. Will argues that it is a mistake to think that 'the future sforeverhidden behind a veil'. He would say that the future s con-stantly being revealed', contraryto Russell's claim that 'We haveexperience of past futures,but not of futurefutures, nd the ques-tion is: Will future futuresresemble past futures?' 440)Will's disagreementwith Russell is apt to getlost in thisquestion ofwhetherwe everactuallyencounterthefuturen its fullfuturity.etterto consider some actual question about the future, uch as whetherBoggs will win. We all know he won't. Is the fact that the event isfuture defeater o thisknowledge claim? Is the reply It hasn't hap-pened yet' a rational response,or just as rationalas the claim thathewon't win? No. Whatever Russell's positionwas, any position whichentails that 'It hasn't happened yet' would suffice to show that oneexpectationwas no worse than its contrary, oth being nothingbetterthan habits of expectationwith no basis in reason, is just silly.Will compares Russell's position to that of someone who makes apromise about next year and then a year later, n reply to the com-plaint that thepromise isn't fulfilled, ays 'This isn't nextyear'. ButRussell has not arranged it so that the future never comes. It's justthatanyfutureyear,from the perspective of a predictor, s differentfromany he has observed, in not being observed (yet). Will says:'The correctconclusion to be drawn from the fact that time passesis that the futureis constantly being revealed and that, in conse-quence, we have had and shall have the opportunityto learn moreand more accurately what the laws of nature's behaviour are andhow therefore he futurewill be like the past'. (449) Russell does notdeny that the future is constantly being revealed. He only denies

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James Cargilethat what we see of it could provide a basis forknowledge about theunrevealed part, unless we can appeal to PI.One possible distraction is that Russell, when writingabout themetaphysics of time, denies that 'past' 'present' and 'future' markgenuine features of reality.This need not concern us here. He willgrant that 'we' exist at a certain time and that relative to that timethere is a 'future',etc. Russell's rejectionof an absolute future s, ifrelevant at all, just reason to say that he would grant Edwards andWill that there is no intrinsicdifferencebetween past futures andfuture futures. There is some difference between what has beenobserved and what has not yetbeen observed. Sometimes a sampleof observed things is a good guide to how thingsare with respect tosome as yetunobserved things. Russell does not denythis any morethan Will does. The question is as to what role the PI plays in thisguidance.Russell's claim that the rationalityof belief in general laws is'completely dependent on the inductive principle' is false. The'inductive principle' is an overgeneralizationof no use by itself informing expectations and laws. But Will's reply is unfortunatelydirected or at least, not at all clearly not directed) at establishing thatthe inductiveprinciple is, after ll, a good one. Will is right n sayingthat we have the opportunity o learn how the futurewill be like thepast,' and even to know this in advance. But this is not achieved oreven facilitated by assuming that 'nature is uniform' or that 'thefuturewill be like the past'. In some ways it will, in some it won't.'The inductiveprinciple' does not help in determiningwhich.Will is sensitive to the point that the general principle is dubious.Of the closely related 'Principle of the Uniformityof Nature', hesays: 'It is ... difficult o interpretthis so-called Principle in such away that it makes a statementwhich is both definiteand is not at thesame time refuted in some areas of experience'. (444) This is anunderstatement.PI is simply a false generalization, so that search-ing for ts basis in reason or deploring its lack of one is deeply mis-guided. This can be obscured by confusing the question whetherthe principle is true in general with the question whetherany par-ticular cases of it are reasonable. It is true that it is often reasonableto regard the next A to be likely or sure to be a B on the groundsthat all past A's have been observed to be B's. The rationalityof aparticular inferencefollowingthe formof the principle is not guar-anteed merely by its being of that form, but other backgroundinformationwhich has not been represented formally.The mistake of thinking that all instances of PI are justifiedmerely by being of that form leads to a further mistake. Onebecomes aware of the firstmistake and moves to the view that no270



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The Problem of Inductioninstances fPI are ustified.The idea would be that f induction' sto be ustifiedt mustbe bythe generic owerofPI. Once it s seenthat PI does not have therequiredgenericpower, t is then con-cluded thatnothing of that form s justifiedunless some othergeneric ourceof authorityan be found.One boost to thisgeneral cepticism s thefollowing act: nytimeanyone ppeals to the fact hat all pastA's have been B's to ustifyconcluding hat ll are or thenextwill be,there s a contraryonclu-sionthat s equally supported y the samefacts et a B* be definedas a thing hat s either xaminedbefore and a B or notexaminedbefore and nota B. Now,whenever ll observedA's areB's, for heright hoiceof t, it is equallytruethat ll observedA's areB*'s. SoPI equally ustifies he conclusions, oththat ll A's are B's, and thatall A's are B*'s. Similarly or he nextA beinga B vs. itsbeinga B*.Butthese onclusions re ncompatible, eing ogicalcontraries. orthenextA tobe a B*, since t s now after , t mustnotbe a B.This is a logically ondensedcase of the generalproblemof thereferencelass.You wantto knowwhether is a B. You know ts anA, andtheyhaveall been B's. But ts also a C, a D, etc. andthey achhave differentatiosof being B's. So whichone shouldyouchooseas your guide?Should you ust averagethemall? A better ugges-tion,in myopinion,is to note that the description f the back-groundconsiderations hatmake one referenceelevantnd anoth-ernotare resistant o characterization ithformal enerality.his'contextdependence' viewgoesbacktoAristotle nd is behind thegeneral cepticism f rationalists bouttheapplicability f univer-sal exceptionless ules to concrete articular ases.Goodman's famous grue' is ust one case of a B*. Goodman is adistinguished ritic f PI. But he shareswiththephilosophers is-cussed earlier tendency o overgeneralizen assessingthesignifi-canceof theprinciple.Goodman describes 'new riddleof induc-tion' as 'theproblem fdistinguishingetween rojectiblend non-projectible ypotheses'1. his projectings ust inferringnd a pro-jectible hypothesiswilleither onstitute,r allow easyconstructionof,a justified nference bout the unobserved,whatwould havebeen called a justified nductive nference. o Goodman,aftermak-ing veryclear that thePI willnot do, is backto seeking genericjustification or nduction.His answer ppearstobe as follows:

To speakvery oosely, might ay that n answer o the questionwhatdistinguishes hoserecurrent eatures f experiencewhich" Nelson Goodman Fact Fiction and Forecast, 2nd edition, (Bobbs-Merill, 1995), p. 83.

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James Cargileunderlie valid projections fromthose which do not, I am suggest-ing thatthe former re those features forwhich we have adoptedpredicates that we have habitually projected. (p. 97)

Goodman bases this conclusion on his famous example of a B*, thepredicate 'grue', meaning 'observed before t and green or notobserved before t and blue'. Before t, all emeralds have been bothgreen and grue, so that PI gives the basis forincompatible projec-tions about future emeralds. Goodman is suggesting that the onlything that ustifies us in predicting the next emerald will be greenrather than grue (and thus, for the right choice of t, not green,butblue) is thatwe are in the habit of using the term green' in predic-tions, while we are not in the habit of using 'grue'. That is, he goesback to Humeanism.QualifyingthePI so as to project only predicates we have been inthe habit of projecting successfully in the past would reduce thenumber of unreasonable projections that would be sanctioned.However, the fact that a predicate is one we are in the habit of suc-cessfullyprojecting does not protect us against the riskof making afoolishmistake about projecting it in some case. And the qualifiedPI would be just as mistaken as ever about the source of the ratio-nality of such projections of ours as are rational ones. Scientistsmay coin a new predicate expressing a neverbefore noticed proper-ty, ay, of atomic particles. They may then predict that all particlesof Kind K will satisfy his predicate, say, alpha'. To project insteada B* for 'alpha' could be seen to be irrational with no referencewhateverto our past habits with regard to the projection of 'alpha',therebeing no such habits.

Against Goodman, it may be objected that grue' is not a purelyqualitative property. For past values of t, emeralds have turned outto be green and not grue aftert,the arbitrary ut-off date built into'grue'. Goodman replies 'I simply do not know how to tellwhethera predicate is qualitative or positional except perhaps by complete-ly begging the question at issue'. He gives an argument: 'grue' and'bleen' are indeed defined in terms of a cut-off date. But 'green' and'blue' can be defined in the same way. For example, X is green iff tis eitherexamined before t and grue, or not examined before t andbleen. Goodman concludes 'Thus qualitativeness is an entirelyrel-ativematterand does not by itself establish any dichotomyof pred-icates.' (p. 80)This is a bad argument." The fact that it is possible to define a

12 I have criticized this argument in 'On Goodman's Riddle ofInduction' Ratio 1970, 144-8.272



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The Problem of Inductionpredicate by reference o a cut-off date does not establish that deter-mining the date is necessary to verify hat the predicate applies. Itis this latter feature that establishes that a predicate is not purelyqualitative. It is possible to tell that something is green even if youhave no idea of the date. It is not possible to tell that something isgrue (on your own authority-you may of course be assured of it byan angel, etc.) withoutknowing the date. Perhaps it is logically pos-sible that someone has sensory mechanisms thatkeep track of howmuch timehas elapsed since the birth of Christ (or anyotherdatingevent). And these mechanisms may be crossed up with his colourperceptions in such a way that aftert, newly discovered emeraldslook different.He would also have to be sensitive to whether a thinghas been previously observed, so thatpreviously observed emeraldswould continue looking like theyused to look.Such a person might well have severe problems gettinghis lan-guage in step with ours, if he had been one of us all along. It wouldtake some ingenuityto work out thehypothesisthathe was a personfor whom 'grue' (or some translation of that term) was a purelyqualitative predicate. Even if this is possible, its being logically pos-sible for grue' to be purely qualitative does notmake itpurely qual-itative. Furthermore, the bare logical possibility for colour predi-cates does not generalize to otherpredicates.Consider the predicate 'dfalls',where X dfalls iffX is observedbefore t and falls or is not observed before t and doesn't fall. Thenall suicide jumpers (without parachutes, etc.) have been observed tofall,but also, up to t, have been observed to dfall as well. Now it isafter t and you are an addicted bungee jumper who is depressed atnot being able to affordthe bungee. Friends argue thatyou shouldjust jump anyway,on the grounds that, like as not, you will justdfall, like everyone has done so far since time immemorial. Oragain, the predicate 'dfirsts' meaning 'observed before t and doesnot finish firstor not observed before t and does finishfirst'. Allrunners broken up in car crashes have failed to finish first n racesheld the next day. But theyhave also all dfirsted. So some followerof PI concludes that there is equal reason to believe that Boggs willdfirst s to believe that he will not finishfirst.One differencebetween these B*'s and 'grue' is thattheyinvolveextensive consequences in a way that colour properties do not. It isnot possible to make coherent a picture of someone for whom suchpredicates could qualify ust as well as 'falls' or 'finishes first,' s notdependent on an arbitrarycut-off date. (No doubt 'winning' is not'purely qualitative,' or 'observational', but the idea behind theobjection about being purely qualitative was surelyto complain thatthe B* predicates involved an arbitrarycut-offdate.)

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James CargileGoodman's position is that the absurdity of these projections isdue to their nvolving predicates we have not developed the habit ofapplying in successful projections. It is of course true that we havenot developed such habits. But it is perfectlypossible logically thatwe should develop such habits without at all incurringthe illusionthat projecting these predicates after t would be anythingbut irra-tional. We mightfind that speaking in terms of 'dfalls' and 'dfirsts'keeps us on our toes about the date. The excitement might lead usto use such predicates heavily, in singular predictions about thebehaviour of thingswe know will be observed safely before t. If wewanted universal laws independent of the time, the use of B* pred-icates would require skill in formulation. The use would be highlyderivative and dependent on less esoteric terminology,but this isstill compatible with getting habitual and successful use. Suchhabits would not give us any reason to expect that any patterns ofprojection would become reasonable which would not be reasonablewithout those habits (excepting of course predictions about whathabits we will be exhibiting).Russell held that the status of PI is problematic. Edwards andWill and Strawson present argumentswith theupshot thattheprin-ciple is true,even analyticallytrue (though some seem not to recog-nize that this is what theyare doing). They do this in spite of giv-ing clear indications of rejecting the idea that induction needs orcan be given a generic justification. That they none the less veerback to the generic is an indication thatthe tendency is deep rootedand difficult o curb. Generalized warnings against overgeneraliza-tion are apt not to be sufficient.Goodman offers n excellent show-ing that if the PI were a general truth,then in a perfectlypossiblecase we could derive inconsistent results about what is justified. Butthen he concludes that the consequences of PI not being a generaltruthare about the ones Hume claimed. Here again is a mistakenestimate of what turns on the truthof PI.If I were to toss a coin repeatedlyand kept gettingheads, I wouldno doubt be deeply impressed, and come to believe that there wassomething about the tossing setup that guaranteed heads. I wouldbe mystified,and yet the pattern of habit formation would go towork,so thatthe coin's behaviour mightcome to seem another inex-

plicable commonplace. If asked to justify my expectations, I couldoffernothing but what would sound like a case of PI. Whether ornot I would be justified, I would certainlybe excusable forformingthe expectation I did form.This suggests that in some cases, merepast positives, etc. in the style of PI would have some weight in thebare way they are held to have weight in the PI. But to generalizefrom such a consideration is to risk losing sight of the rich variety274



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The Problem of Inductionof inductive reasoning. One may begin to see constantconjunctionscropping up through thevarietyof inductions and thenvastlyover-estimate their mportance in the critical assessment of the inductiveperformance.The tendency to think that one has discovered a testfor the truth of claims to knowledge is endemic in Epistemologyand provides occasions forcriticsof the subject to accuse its practi-tioners of delusions of grandeur. That branch of Epistemologywhich 'confines' itself to induction has been afflictedwith some ofthe worst outbreaks of the tendency.University f Virginia

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